Research progress on the mathematical model of groundwater flow and solute transport in fractured rock
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Abstract:
With the continuous intensification of human activities and the continuous development of groundwater science, it is more and more crucial to study the water and solutes transport of fractured soil or rocks in groundwater remediation, agriculture engineering, underground construction, fractured reservoir industry and geological carbon storage (GCS). The different research ideas and research methods are reviewed and the latest research findings on the multi-physics coupled model of groundwater flow and solute transport in fractured rock are summarized.According to the generalization of fractured media, all the fractured models can be divided into (1) Equivalent Porous Model, (2) Multi-continuum Models, (3) Discrete Fracture Model.The Equivalent Porous Model use the equivalent permeability, which makes the model degenerate into a simple model like the ideal porous model, and the validity of the model is often questioned. The Multi-continuum Model is a kind of model that uses the overlapping of multiple media to represent fractured porous media. These different media use different equilibrium equations and transport laws. The calculation of exchange term (for example pore-fracture exchange) is a key of the Multi-continuum Model. These models may achieve a balance in simplification of calculation and capturing different characteristics in fracture and pore matrix. The Discrete Fracture Model is a kind of model that explicitly models fractures. It is generally necessary to determine the specific distribution of each fracture. According to whether the permeability of the pore matrix is considered, it can be further divided into the discrete fracture matrix model (DFM) and discrete fracture network model (DFN). The Discrete Fracture Model has advantages for multi-physics coupling, but the calculation is rather complicated.The multi-physics coupled model can generally be divided into the (1) fully coupled model and (2) non-fully coupled model according to whether each physics is completely bidirectionally coupled.The non-fully coupled model generally refers to that the partial differential equations of different physics are only loosely connected, or only consider the one-direction influence between different physics. The classical solute transport model only considers the convection and dispersion of a solute in the fluid, ignoring the influence of solute concentration on the hydraulic field (such as density change and chemical osmosis). Terzaghi’s consolidation theory and its related models do not consider the fully coupling behavior between the hydraulic and the mechanical field.A fully coupled model needs to consider all the controlling physics of specific behavior and establishes the coupling equations of all variables, and its description of coupling behavior is the most accurate one. The study of the fully coupled model of hydraulic-mechanical behavior begins with Biot. After Biot, researchers modified the equation of rock deformation, and permeability, and considered multiphase flow. More physics fields are also added to the hydraulic-mechanical coupled model. These kinds of models are mainly derived based on the basic principles of rock force balance, fluid mass balance, and momentum conservation, normally named Mechanical Approach models. But when it comes to the study of solutes, due to the gap between geophysics and geochemistry, the Mechanical Approach often lacks unity in the theoretical framework.The Mixture Coupling Theory overcomes the above shortcoming and provides a unified theoretical framework by associating different physics with free energy and taking entropy production as the only driving force. Since the permeability of the pore matrix in fractured rocks is often very low, the coupling effect between fluid, solute and heat transport can not be ignored. The Mixture Coupling Theory can easily give the coupling transport law of different physics using the entropy production in the system. It is shown that Darcy’s law, Fick’s law and Fourier heat transfer law are approximations without considering the coupling of other transport phenomena.It is suggested that the future research direction of the new multi-physics coupling model of fractured groundwater flow and solute transport is mainly concentrated on: Study of the coupling mechanism of different behaviors in multi-space scales and multi-time scales of fracture media; Study on groundwater coupling model under large rock deformation; Accurate description of fracture distribution and random fracture modeling research.
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